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Minerals Engineering 20 (2007) 349–354

Air core formation in the hydrocyclone

T. Neesse *, J. Dueck

Department of Environmental Process Engineering and Recycling, University Erlangen-Nuremberg,

Paul-Gordan-Str. 3, D-91052 Erlangen, Germany

Received 1 August 2006; accepted 15 January 2007Available online 20 February 2007

Abstract

Air core formation has been investigated in hydrocyclones operated with clear water and a lucid suspension of glass balls. Hydrocy-clones form a central air core which extends over the complete hydrocyclone length. Air is sucked in the core at the underflow discharge.The air core diameter can be determined balancing the positive pressure gradient and the centrifugal force in the rotational flow field. Indense flow separation (high feed solids content) the air core in the conical part of the hydrocyclone is suppressed. The hydrocyclone oper-ates as it is air sealed because the solids are discharged trough the underflow as a rope. Then, air can be introduced to the hydrocycloneonly on the feed side. In practice, feed suspension always contains more or less dissolved or dispersed air. Observations in a transparenthydrocyclone show that dissolved gas is released due to the pressure drop inside the hydrocyclone. The generated micro bubbles grow bycoalescence and move in the centrifugal field toward the centre, where an air core is formed.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Hydrocyclone; Classification; Modelling; Fine particle processing

1. Introduction

Air is the often the neglected third phase of the 3-phaseflow in the hydrocyclone. The air core at the center of thehydrocyclone is an unavoidable phenomenon in the rota-tional flow field which does not directly influence the clas-sification process in the apparatus. However, this isdifferent in new applications of the apparatus to flotation(Puget et al., 2004) and to separations in multi-phase sys-tems involving vapors and gases (Madge et al., 2004) wherethe air core plays a more active role. Furthermore, thegeometry and movement of the air core were identified asbeing sensitive indicators of the operational state of hydro-cyclones (Neesse et al., 2004a,b,c). Therefore, in recentyears studies on the air core in hydrocyclones have beenthe subject of intensive research. At present, the knowledgeon air core behaviour is limited and based mostly on obser-

0892-6875/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2007.01.007

* Corresponding author. Tel.: +49 0 9131/85 23 200; fax: +49 0 9131/8523 178.

E-mail address: thomas.neesse@uvt.cbi.uni-erlangen.de (T. Neesse).

vations in transparent hydrocyclones (Ternovsky andKutepov, 1994). Air core monitoring using electricalimpedance was carried out by Williams et al. (1995).Numerous data on air core diameters dependent on hydro-cyclone parameters were collected and summarised inempirical and semi-empirical formulas by Abduramanov(1986), Barrientos et al. (1993), Castro et al. (1996), David-son (1995), Povarov (1961) and Ternovsky and Kutepov(1994). However, only a few theoretical investigations onthe subject were published by Dreissen (1951), Dyakowskiand Williams (1995) and Steffens et al. (1993). Therefore,the complex process of air core formation starting frominstabilities of the multiphase flow up to the stable air coreremains poorly understood and described. Here, we reportsome recent findings providing new insights into this highlycomplex mechanism.

2. Air flow through the hydrocyclone

Fig. 1 presents schematically the air balance of thehydrocyclone. Generally, two ways of air input can be

Disintegration of Air core

Breather tube

Air core

Air with feed

Releasedmicro bubbles

Air from spigot

Aerosuspension

Fig. 1. Air balance in the hydrocyclone.

Table 1The hydrocyclone and feed parameters for the computer simulation

Hydrocyclone diameter 150 mmInlet nozzle 25 · 80 mmVortex finder 72 mmDepth of the vortex finder 100 mmWall thickness of the vortex finder 5 mmSpigot diameter 38 mmLength of the spigot 150 mmHeight of the cylindrical section 350 mmCone angle 18�Feed pressure 1 barSolids content in the feed mixture 100–400 g/lMaximum particle size in the feed 1 mm

350 T. Neesse, J. Dueck / Minerals Engineering 20 (2007) 349–354

distinguished. In dilute flow separation (spray discharge inthe underflow) air is sucked through the spigot to thecentre of the hydrocyclone. However, also feed suspensionalways contains a certain amount of air in a dispersed ordiluted form. As illustrated later, this amount of air alsocontributes to the air core formation.

The steady air input causes a continuous air flowthrough the core upwards to the overflow. In the overflowpipe the centrifugal force is reduced thus not enabling a sta-ble air core further to exist. Hence, the air core is disinte-grated to bubbles which are discharged with the overflow.

3. Air core formation in separation of dilute flow

If a suspension is pumped to a hydrocyclone the air coreat the centre is formed due to the force balance in the flow.In dilute flow separation (low feed solids content) this aircore extends over the complete length of the hydrocycloneending as spray discharge in the underflow. This dischargeshape can be described with the discharge angle a whichhas been computed by Neesse et al. (2004c) according tothe following relation:

a ¼ arctanvu� arctan

qmDu2

w2

lm

� �:

Here, u, v, w are the axial, radial and tangential suspensionvelocities, qm is the density, lm is the effective viscosity of

the suspension and Du is the spigot diameter. These quan-tities were computed at the spigot exit using the simulationof Dueck et al. (2000) which is based on the Navier–Stokesequations, considering the reaction of the solids content ofthe suspension on the flow parameters.

A spray discharge at the spigot exit can only exist if atthis point the axial velocity is negative meaning, it is direc-ted inside the hydrocyclone toward the overflow. This is acondition for air sucking through the underflow. The sim-ulation at the spigot exit was conducted with the data of a150 mm hydrocyclone listed in Table 1. As shown in Fig. 2an air core at the spigot exit only occurs in dilute suspen-sions (solids content in the feed 100 g/l). At 400 g/l theaxial velocity indicates positive values over the completeradius resulting in rope discharge. At the transition pointthe axial velocity oscillates around zero value and causesdiscontinuous air suction into the hydrocyclone.

3.1. Stable air core

Under stable conditions the air core is characterised byconstant dimensions. The core diameter can be determinedbased on the radial pressure distribution in the hydrocy-clone considering the radial projection of the Navier–Stokes equations at steady-state:

dpdr¼ ql

v2u

r: ð1Þ

where p is the pressure, ql is the liquid density, vu is the tan-gential velocity and r is radial coordinate in thehydrocyclone.

Eq. (1) indicates that the positive pressure gradient isbalanced by the centrifugal force.

The integration Eq. (1) leads to:

pðRÞ ¼ pin �Z Rc

Rql

v2u

rdr; ð2Þ

where pin is the pressure at the inlet and Rc is the nominal

radius of the hydrocyclone. The term �R Rc

R qlv2u

r dr denotesthe pressure drop between Rc and R.

In Eq. (1) for vu a semi-empirical relationship of Heiska-nen (1993) or Ternovsky and Kutepov (1994) can be used:

Fig. 2. Calculated axial velocity at the spigot exit of a 150 mmhydrocyclone.

0.4

0.5

0.6

0.7

0.8

0.05 0.1 0.15 0.2 0.25 0.3

Ro/Rc

Ra/R

o

Calculation based on Eq.(10)

Measurements of Povarov (1961)

Fig. 3. Comparison of theoretically (Eq. (10)) and experimentally(Povarov, 1961) determined air core radii.

Table 2The parameters of the hydrocyclone used for the air core measurements

Hydrocyclone diameter 75 mmInlet nozzle 18 mmVortex finder 25 mmSpigot diameter 10 mmLength of the spigot 150 mmHeight of the cylindrical section 300 mmCone angle 9�

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2pin [bar]

Ra/R

c [-

]

Calculation based on Eq. (8)

Experimental data

Fig. 4. Air core diameter in a 75 mm water hydrocyclone versus feedpressure (p0 = 0.2 bar).

T. Neesse, J. Dueck / Minerals Engineering 20 (2007) 349–354 351

vuðrÞ ¼ vwRc

r

� �n

; ð3Þ

where vw is the tangential velocity at the hydrocyclone en-trance. Heiskanen (1993) and Ternovsky and Kutepov(1994) determined the constant being n = 0.8.

Setting Eq. (3) in Eq. (2) and integrating from Ra to Rc

and further, assuming that the pressure at the core bound-ary is equal to pu yields:

Ra

Rc

¼ 1þ 2nql

pin � pu

v2w

� �1=2n

: ð4Þ

According to Joshioka and Hotta (1955), the tangentialvelocity vw at the hydrocyclone entrance can be empiricallyapproximated as follows:

vw ¼ 3:7Rin

Rc

� �uin; ð5Þ

with Rc, Rin, being the radii of the hydrocyclone and thefeed nozzle, and uin is the velocity at the inlet, which isdetermined by the hydrocyclone throughput Q accordingto the relation of Ternovsky and Kutepov (1994):

Q ¼ pR2inuin ¼ 4kR2

in

Ro

Rin

� �m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipin � p�a

ql

r: ð6Þ

where Ro is the overflow radius and p�a is the effective dou-ble pressure drop due to the two discharges of the hydrocy-clone. Considering that the hydraulic resistance in theoverflow normally being higher than in the underflow, itcan be assumed: p�a � po.

According to Heiskanen (1993), Povarov (1961) andTernovsky and Kutepov (1994) the empirical constants kand m depend on hydrocyclone geometry. As mean valuesk = 0.27 and m = 1 are representative.

Thus, from Eq. (6) yields uin ¼ 4kp

Ro

Rin

� �m ffiffiffiffiffiffiffiffiffiffipin�po

ql

qand Eq.

(5) changes to:

vw ¼14:8k

pRin

Rc

� �Ro

Rin

� �m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipin � po

ql

r: ð7Þ

Combining Eqs. (7) and (4) leads to a dimensionless rela-tion for the air core radius Ra as function of hydrocyclone

radius Rc, inlet radius Rin, overflow radius Ro and the pres-sures in the spigot pu and in the overflow po:

Ra

Rc

¼ 1þ 2n

k2w

Rc

Rin

� �2 Rin

Ro

� �2m pin � pu

pin � po

� �" #�1=2n

: ð8Þ

With k = 0.27 the constant in the previous equation iskw ¼ 14:8k

p ¼ 1:28.In case of high inlet pressure and free discharge

pin�pupin�po

� 1� �

from Eq. (8) follows, that Ra depends only

on geometrical parameters of the hydrocyclone:

352 T. Neesse, J. Dueck / Minerals Engineering 20 (2007) 349–354

Ra

Rc

¼ 1þ 2n

k2w

Rc

Rin

� �2 Rin

Ro

� �2m" #�1=2n

: ð9Þ

For m = 1 and n = 0.8 Eq. (9) can be converted to

Ra

Ro

¼ Rc

Ro

� �1þ 0:975

Rc

Ro

� �2" #�0:625

:

The previous equation can be approximated as

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.25 0.5 0.75 1

po [bar]

Ra/R

c [-

]

Calculation based on Eq. (8)

Experimental data

Fig. 5. The dependency of air core diameter in water hydrocyclone onpressure in the overflow (pin = 1.2 bar).

Fig. 6. Air core in the conical part of the hydrocyclone for a glass balls

Ra

Ro

¼ 0:48þ 0:85Ro

Rc

: ð10Þ

As can be seen in Fig. 3, calculated radii according to Eq.(10) correspond to the experimentally determined values ofPovarov (1961).

3.2. Experiments

Air core measurements were accomplished at a transpar-ent 75 mm polycarbonate hydrocyclone (Ru/Ro = 0.4,po = 0.2 bar) operated with water. The hydrocycloneparameters are listed in Table 2. Air core diameters wereobtained by evaluation of scaled photographs. Measuredand computed data of the air core diameter dependenton feed pressure and overflow pressure are depicted inFigs. 4 and 5. Fig. 4 illustrates the expected weak depen-dence of the air core radius on feed pressure. The experi-mental data of Fig. 5 confirm the increasing suppressionof the air core with growing overflow pressure accordingto Eq. (8).

4. Air core formation in dense flow separation

Further experiments with the 75 mm hydrocyclone wereconducted using a lucid suspension of 2 mm glass balls.Under these conditions the air core remains visible evenin dense flow separation. Fig. 6a displays a fully developedair core for low solids concentration. In dense flow separa-tion at high feed solids content (Fig. 6b) the hydrocyclone

suspension in a 75 mm – hydrocyclone (inlet pressure pin = 2.0 bar).

T. Neesse, J. Dueck / Minerals Engineering 20 (2007) 349–354 353

operates as it is air-sealed at the underflow. Consequently,the air core terminates in the sediment stored in the conicalpart of the hydrocyclone. Then, air can only penetrate to

Fig. 7. Experimental set up for air core observation with air sealeddischarges of overflow and underflow.

Fig. 8. Air core formation in the hydrocy

the hydrocyclone together with the feed flow. To examinethis operational situation, a special experimental set upwas used by Golyk (2006) which is sketched in Fig. 7. Ina closed hydrocyclone circuit the discharges of overflowand underflow were immersed under the water surface ofthe pump sump. Therefore, no air penetrated the hydrocy-clone from outside. Before starting the pump, the hydrocy-clone was filled with water. The question was whether anair core can develop under these conditions. As shown inFig. 8, a small bubble column became visible in the centreof the hydrocyclone shortly afterwards. Eventually thesebubbles are combined (Fig. 8d and e) to form a small diam-eter-air core. This process can be explained as follows:

Usually, technical suspensions fed to a hydrocyclonecontain a certain amount of air in a diluted form and/oras micro-bubbles. According to Eqs. (2) and (3) a radialpressure drop exists inside the hydrocyclone:

ppin

¼ 1� qL � v2w

2npin

Rc

r

� �2n

� 1

" #:

Due to this pressure drop according to the Henry-law airbubbles are generated in the hydrocyclone. The radial bub-ble transport leads to bubble enrichment and bubblegrowth due to coalescence (Fig. 8a and b). Thus, at the cen-tre single core legs (Fig. 8c and d) are produced which final-ly unify to a small diameter – air core (Fig. 8e).

clone starting from an air suspension.

354 T. Neesse, J. Dueck / Minerals Engineering 20 (2007) 349–354

Due to the stochastic character of bubble coalescence inturbulent flow, the air core is not strongly centred. As canbe seen in Fig. 8 at the central line, the radial air coremovement is characterized by random eccentricity.

5. Conclusions

Geometry and movement of the air core are sensitiveindicators of the operational state and can be used inhydrocyclone monitoring. The air core radius can be esti-mated based on the Navier–Stokes equations assumingthe force equilibrium between pressure gradient and cen-trifugal force at the boundary liquid–gas. This physicalconsideration leads to Eq. (8) which indicates that the aircore radius is primarily determined by the hydrocyclonegeometry. Of practical interest is the question under whichconditions the air core could be suppressed. According toEq. (8) this can be obtained by increasing the pressure inthe overflow. To note, the standard operating conditionsare not taken in account here. However, this may be thecase under special circumstances, i.e. if the hydrocycloneoperates against pressure in a reactor downstream or ifthe overflow is discharged above the level of the overflownozzle resulting in a hydrostatic backpressure. The air coreand the continuous air flow through the apex are inter-rupted if at high solids content the underflow is dischargedas a rope. Then, the air core in the apex region is sup-pressed. Nevertheless, even under these conditions an aircore may exist or might even be formed. Moreover, onehas to consider that air not only penetrates the apparatusthrough the underflow but also through the feed nozzle.In practice every feed suspension contains a limitedamount of air in a diluted form or as micro bubbles. Firstof all, feed air causes the well known twitching movementof the fully developed air core. Additionally, under ropingconditions feed air may even form an air core. A specialexperiment confirmed this process resulting in an air coreof special state. The movement of this small diameter-coreis characterized by random eccentricity. This phenomenonaffects hydrocyclone vibration and can be used in the mon-itoring of the apparatus.

To conclude, air core formation by feed air is a novelfinding which underlines the expectation that in normalfunctioning hydrocylones the total suppression of the aircore seems to be impossible.

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